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Connections, Curvature, and Cohomology
Contents
Context
-Chern-Weil theory
Differential cohomology
differential cohomology
Ingredients
Connections on bundles
Higher abelian differential cohomology
Higher nonabelian differential cohomology
Fiber integration
Application to gauge theory
-Lie theory
∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
This entry is about the book
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Werner Greub, Stephen Halperin, Ray Vanstone:
Connections, Curvature, and Cohomology
Academic Press (1973)
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Volume 1:
De Rham Cohomology of Manifolds and Vector Bundles
ISBN:978-0-12-302701-6
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Volume 2:
Lie groups, principal bundles and characteristic classes
ISBN:9780123027023
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Volume 3:
Lie Algebras, Algebraic Connections and Characteristic Classes
ISBN:9780123027016
on Chern-Weil theory: principal bundles with connections and their characteristic classes.
Related books are
Contents
Volume I
0 Algebraic and analytic preliminaries
1 Basic concepts
II Vector bundles
V De Rham cohomology
VI Mapping degree
VII Integration over the fiber
VIII Cohomology of sphere bundles
IX Cohomology of vector bundles
X The Lefschetz class of a manifold
Appendix A The exponential map
Volume II
0 Algebraic and analytic preliminaries
I Lie groups
II Subgroups and homogeneous spaces
IV Invariant cohomology
V Bundles with structrue group
VI Principal connections and the Weil homomorphism
VII Linear connections
VIII Characteristic homomorphism for -bundles
IX Pontrjagin, Pfaffian, Chern classes
X The Gauss-Bonnet-Chern theorem
Appendix A Characteristic coefficients and the Pfaffian
Volume III
0 Algebraic preliminaries
I Spectral sequences
II Koszul complexes of -spaces and -algebras
III Koszul complexes of -differential algebras
IV Lie algebras and differential spaces
V Cohomology of Lie algebras and Lie groups
VI The Weil algebra
VII Operation of a Lie algebra in a graded differential algebra
VIII Algebraic connections and principal bundles
IX Cohomology of operations and principal bundles
X Subalgebras
XI Homogeneous spaces
XII Operation of a Lie algebra on a pair
Appendix A Characteristic coefficients and the Pfaffian
Last revised on July 16, 2022 at 05:53:22.
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